HPC Adaptive Timestepping: Difference between revisions

|This condition ensures that water entering one side of a 2D cell does not pass through the other side within one timestep. For this to be satisfied, the product of the water velocity (𝑢) and model timestep (∆𝑡) must be less than the cell size (∆𝑥).

|[[FILE: Courant Number Equation.PNG |250px]]

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|style="height:110px;" | The Shallow Wave Celerity <br> Number (Nc)

|This numerical condition relates to the shallow water wave celerity (wave speed) and is derived from the fluid flow equations to represent long waves (i.e. wave length is substantially longer than the water depth). The product of the model timestep (∆𝑡) and the long wave speed (square root of the gravity (g) and water depth (h)) must be less than the cell size (∆𝑥), for the condition to be satisfied.

|[[FILE: SWC Number Equation.PNG |250px]]

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|style="height:80px;" | Diffusion Number (Nd)

|This numerical condition relates to the sub-grid scale eddy viscosity term which causes diffusion of momentum. To maintain stability the product of the eddy viscosity coefficient (ν_T) and the timestep (∆𝑡) divided by the square of the grid spacing (∆𝑥2) must remain below 0.3. Models controlled by the diffusion number tend to require a timestep significantly smaller than those controlled by the shallow wave celerity or courant numbers. If you find your model is predominantly diffusion controlled it may be that equivalent solution accuracy can be achieved by selecting a larger cell size. This is worth testing, as it will most likely increase the simulation speed with no loss of result fidelity.

|[[FILE: Diffusion Number Equation.PNG |250px]]

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